A minimal regular ring extension of C(X)

M. Henriksen; R. Raphael; R. G. Woods

Fundamenta Mathematicae, Tome 173 (2002), p. 1-17 / Harvested from The Polish Digital Mathematics Library

Résumé

Let G(X) denote the smallest (von Neumann) regular ring of real-valued functions with domain X that contains C(X), the ring of continuous real-valued functions on a Tikhonov topological space (X,τ). We investigate when G(X) coincides with the ring $C (X, τ_{δ})$ of continuous real-valued functions on the space $(X, τ_{δ})$ , where $τ_{δ}$ is the smallest Tikhonov topology on X for which $τ \subseteq τ_{δ}$ and $C (X, τ_{δ})$ is von Neumann regular. The compact and metric spaces for which $G (X) = C (X, τ_{δ})$ are characterized. Necessary, and different sufficient, conditions for the equality to hold more generally are found.

Publié le : 2002-01-01

Zbl 0995.46022

EUDML-ID : urn:eudml:doc:283045

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     title = {A minimal regular ring extension of C(X)},
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     volume = {173},
     year = {2002},
     pages = {1-17},
     zbl = {0995.46022},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-1-1}
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M. Henriksen; R. Raphael; R. G. Woods. A minimal regular ring extension of C(X). Fundamenta Mathematicae, Tome 173 (2002) pp. 1-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-1-1/